Some results concerning maximum Renyi entropy distributions

By Oliver Johnson, Christophe Vignat. 2005

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Abstract We consider the Student-t and Student-r distributions, which maximise Renyi entropy under a covariance condition. We show that they have information-theoretic properties which mirror those of the Gaussian distributions, which maximise Shannon entropy under the same condition. We introduce a convolution which preserves the Renyi maximising family, and show that the Renyi maximisers are the case of equality in a version of the Entropy Power Inequality. Further, we show that the Renyi maximisers satisfy a version of the heat equation, motivating the definition of a generalised Fisher information.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c380f5ddc3f5464d96fb5de2829f8cc926e53ae3